Pricing and calibration of CDOs in a multi-dimensional structural jump-diffusion model'

We consider a multidimensional structural credit model, where each company follows a jump-diffusion process and is connected with other companies via global factors. We assume that a company can default both expectedly, due to the diffusion part, and unexpectedly, due to the jump part, by a sudden fall in a company's value as a result of a global shock. To price CDOs efficiently, we use ideas, developed by Bush et al.

for diffusion processes, where the joint density of the portfolio is approximated by a limit of the empirical measure of asset values in the basket. We extend the method to jump-diffusion settings. In order to check if our model is flexible enough, we calibrate it to CDO spreads from pre-crisis and crisis periods.

For both data sets, our model fits the observed spreads well, and what is important, the estimated parameters have economically convincing values.

We also study the convergence of our method to basic Monte Carlo and conclude that for a CDO, that typically consists of 125 companies, the method gives close results to basic Monte Carlo."